Shape Correspondence through Landmark Sliding
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Transcript of Shape Correspondence through Landmark Sliding
![Page 1: Shape Correspondence through Landmark Sliding](https://reader036.fdocuments.in/reader036/viewer/2022070405/56813ce7550346895da691e3/html5/thumbnails/1.jpg)
Anup Kedia
Shape Correspondence through Landmark Sliding
Anup Kedia
![Page 2: Shape Correspondence through Landmark Sliding](https://reader036.fdocuments.in/reader036/viewer/2022070405/56813ce7550346895da691e3/html5/thumbnails/2.jpg)
Introduction
• Shape• Landmarks
![Page 3: Shape Correspondence through Landmark Sliding](https://reader036.fdocuments.in/reader036/viewer/2022070405/56813ce7550346895da691e3/html5/thumbnails/3.jpg)
Contd..
• Landmark Sliding• Shape Correspondence
• Result
![Page 4: Shape Correspondence through Landmark Sliding](https://reader036.fdocuments.in/reader036/viewer/2022070405/56813ce7550346895da691e3/html5/thumbnails/4.jpg)
Need
• Statistical Shape Analysis
• Accuracy
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Different types of Shapes
• Supports closed, open, self-crossing and multiple shapes.
![Page 6: Shape Correspondence through Landmark Sliding](https://reader036.fdocuments.in/reader036/viewer/2022070405/56813ce7550346895da691e3/html5/thumbnails/6.jpg)
Input
• Landmarks of template shape
• Landmarks of target shape
• The shape is open or closed
![Page 7: Shape Correspondence through Landmark Sliding](https://reader036.fdocuments.in/reader036/viewer/2022070405/56813ce7550346895da691e3/html5/thumbnails/7.jpg)
Contd..
• The parameters are
is the curve length from u(0) to u(t)
s|L is the curve length from v(0) to v(s)
a|b modulus operation
GOAL : To find s = {s0 , s1 , … sn-1 } such that the shape ‘V’ (target) from it corresponds well to the template shape.
![Page 8: Shape Correspondence through Landmark Sliding](https://reader036.fdocuments.in/reader036/viewer/2022070405/56813ce7550346895da691e3/html5/thumbnails/8.jpg)
Problem
• How to represent the shape?
• We use Catmull Rom Splines since
a. They are smooth
b. They interpolate the landmarks.
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Problem
• How to represent and initialize the landmarks?
We manually label the landmarks s.t1. The no. of landmarks are same2. The starting pt. is approximately the
same.i.e , we roughly correspond the landmarks
manually.
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Contd..
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Problem
• If a landmark moves beyond its neighbours?
We add a constraint
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Goal
• We try to minimize the cost function,
Ø(s) = d(U,V) + λR(s)
d(U,V) -> landmark based shape difference
R(s) -> representation Error
λ -> Regularization Factor
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Contd..
L Thin Plate matrix
λ = 10-3 in our experiments
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Experiment
![Page 15: Shape Correspondence through Landmark Sliding](https://reader036.fdocuments.in/reader036/viewer/2022070405/56813ce7550346895da691e3/html5/thumbnails/15.jpg)
Open Shapes
• For open curves, we
1. Fix the end points
2. Remove segment between the first and last point while calculating R(s).
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Experiment for open shapes
![Page 17: Shape Correspondence through Landmark Sliding](https://reader036.fdocuments.in/reader036/viewer/2022070405/56813ce7550346895da691e3/html5/thumbnails/17.jpg)
Multiple Curves
1. ‘L’ is calculated taking all the curves.
2. R(s) is calculated seperately for each curve.
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Experiment for multiple curves
![Page 19: Shape Correspondence through Landmark Sliding](https://reader036.fdocuments.in/reader036/viewer/2022070405/56813ce7550346895da691e3/html5/thumbnails/19.jpg)
Multiple Shape Correspondence
• We have a set of samples We have to find an average shape to which all the shapes corresponds well.
• We do it by1. Taking average of all the shapes using
procustes analysis2. Slide the shapes w.r.t to the average shape3. Repeat the above process.
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Experiment
![Page 21: Shape Correspondence through Landmark Sliding](https://reader036.fdocuments.in/reader036/viewer/2022070405/56813ce7550346895da691e3/html5/thumbnails/21.jpg)
Conclusion
• Works for all types of shapes
• It considers both global shape deformation and local geometric features unlike the previous methods.